With the Nerevarine, I'm not too certain, but they weren't the same thing or close to what the Drasgonborn is in theory or practice. What I mean is, what the Nerevarine did, made him that way. Initially, nothing set him apart from others.
The Champion of Cyrodiil on the other hand, is unfortunately to me, a more "Anyman" role. Basically, the Hero is just some trustworthy guy who delivers an amulet, and can handle himself in combat. He has no special soul/powers that really set him that far apart from Bandits, or Marauders. In fact, sometimes he could be ill-suited, because he was so.... nameless. He was "The Hero of Kvatch" and etc. but something was lacking where the Nerevarine had a sort of... spice.
Now the Dovahkiin (Sp?) is different.
He was born with the soul of a Dragon. In other words, he was popped out like that, as opposed to "made" that way. Like, at 20 years old, he doesn't just decide to be the Dragonborn... And, he has this huge prophecy built on and around him, so he must have some significance as opposed to the Hero of Kvatch. He could contend, or oust the Nerevarine IMO.